Question

perform the following conversions using the value 6.8×10³ k, which is the surface temperature of the sun. part 1 of 2 convert to °c. be sure your answer has the correct number of significant figures. part 2 of 2 convert to °f. be sure your answer has the correct number of significant figures.

Explanation:

Step1: Recall temperature - conversion formula

The formula to convert Kelvin (K) to Celsius ($^{\circ}C$) is $T_{C}=T_{K}- 273.15$. Given $T_{K}=6.8\times10^{3}\text{ K}$.

Step2: Perform the calculation

$T_{C}=6.8\times10^{3}-273.15 = 6800 - 273.15=6526.85^{\circ}C$. Rounding to two - significant figures (since the given value $6.8\times10^{3}$ has two significant figures), we get $T_{C}=6.5\times10^{3}^{\circ}C$.

Step3: Convert Celsius to Fahrenheit

The formula to convert Celsius to Fahrenheit is $T_{F}=\frac{9}{5}T_{C}+32$. Substitute $T_{C}=6.5\times10^{3}^{\circ}C$ into the formula: $T_{F}=\frac{9}{5}\times(6.5\times10^{3})+32$. First, $\frac{9}{5}\times(6.5\times10^{3}) = 1.8\times6.5\times10^{3}=11.7\times10^{3}=11700$. Then $T_{F}=11700 + 32=11732^{\circ}F$. Rounding to two - significant figures, $T_{F}=1.2\times10^{4}^{\circ}F$.

Answer:

Part 1: $6.5\times10^{3}^{\circ}C$
Part 2: $1.2\times10^{4}^{\circ}F$